Training sequence for a radio communications system

ABSTRACT

A training sequence for a radio communications system is provided. According to one aspect of the present invention, the invention includes a core sequence of symbols, a successive repetition of the core sequence, and a marker sequence having a sequence of symbols different from the core sequence.

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application is a continuation of U.S. patent applicationSer. No. 09/727,063, filed Nov. 30, 2000.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] The present invention applies to the field of training sequencesfor radio communications systems and, in particular, to a trainingsequence having a unique periodic structure.

[0004] 2. Description of the Prior Art

[0005] Mobile radio communications systems such as cellular voice anddata radio systems typically have several base stations in differentlocations available for use by mobile or fixed user terminals, such ascellular telephones or wireless web devices. Each base station typicallyis assigned a set of frequencies or channels to use for communicationswith the user terminals. The channels are different from those ofneighboring base stations in order to avoid interference betweenneighboring base stations. As a result, the user terminals can easilydistinguish the transmissions received from one base station from thesignals received from another. In addition, each base station can actindependently in allocating and using the channel resources assigned toit.

[0006] Such radio communications systems typically include a broadcastchannel (BCH). The BCH is broadcast to all user terminals whether theyare registered on the network or not and informs the user terminalsabout the network. In order to access the network, a user terminalnormally tunes to and listens to the BCH before accessing the network.It will then use the information in the BCH to request access to thenetwork. Such a request typically results in an exchange of informationabout the network using separate control and access channels and ends inthe user terminal receiving an assignment to a particular base station.

[0007] While frequency and timing offset can sometimes be determined bya user terminal based on the BCH, the initial request for access istypically received at the base station with an unknown amount of delayand unknown spatial parameters. In a spatial diversity multiple accesssystem, the base station can enhance the capacity of the system bydetermining the position and range to the user terminal as well as anyother spatial parameters. The delay in the arrival time of such requestmessages are proportional to the round trip delay encountered bymessages traveling between the base station and the mobile terminal. Forsystems with a high coverage area per base station, this range andtherefore the delay uncertainty may be very large. For example, a rangeof fifteen km results in a roundtrip delay time of around 100microseconds.

[0008] In order to accurately resolve the access request and determinespatial parameters, a training sequence is typically transmitted withthe request. Resolving the received signal using the training sequencecan consume great computational resources and create delays in the basestation's response to the request. The greater the uncertainty of thereceived signal, the greater the computational resources that may berequired.

BRIEF SUMMARY OF THE INVENTION

[0009] A training sequence for a radio communications system isprovided. According to one aspect of the present invention, theinvention includes a core sequence of symbols, a successive repetitionof the core sequence, and a marker sequence having a sequence of symbolsdifferent from the core sequence.

BRIEF DESCRIPTION OF THE DRAWINGS

[0010] The present invention is illustrated by way of example, and notby way of limitation, in the figures of the accompanying drawings inwhich like reference numerals refer to similar elements and in which:

[0011]FIG. 1 is a simplified block diagram of a base station on which anembodiment of the invention can be implemented;

[0012]FIG. 2 is a block diagram of a remote terminal on which anembodiment of the invention can be implemented;

[0013]FIG. 3 is a diagram of an exemplary broadcast channel BCH burst;

[0014]FIG. 4 is a diagram of an exemplary configuration request CRburst;

[0015]FIG. 5 is a diagram of an exemplary training sequence inaccordance with the present invention;

[0016]FIG. 6 is a flow chart of an implementation of aspects of thepresent invention;

[0017]FIG. 7 is a graph of a search for a least squares error relativetiming; and

[0018]FIG. 8 is a graph of a follow-up search for a least squares errorrelative timing.

DETAILED DESCRIPTION OF THE INVENTION

[0019] Base Station Structure

[0020] The present invention relates to wireless communication systemsand may be a fixed-access or mobile-access wireless network usingspatial division multiple access (SDMA) technology in combination withmultiple access systems, such as time division multiple access (TDMA),frequency division multiple access (FDMA) and code division multipleaccess (CDMA). Multiple access can be combined with frequency divisionduplexing (FDD) or time division duplexing (TDD). FIG. 1 shows anexample of a base station of a wireless communications system or networksuitable for implementing the present invention. The system or networkincludes a number of subscriber stations, also referred to as remoteterminals or user terminals, such as that shown in FIG. 2. The basestation may be connected to a wide area network (WAN) through its hostDSP 231 for providing any required data services and connectionsexternal to the immediate wireless system. To support spatial diversity,a plurality of antennas 103 is used, for example four antennas, althoughother numbers of antennas may be selected.

[0021] A set of spatial multiplexing weights for each subscriber stationare applied to the respective modulated signals to produce spatiallymultiplexed signals to be transmitted by the bank of four antennas. Thehost DSP 231 produces and maintains spatial signatures for eachsubscriber station for each conventional channel and calculates spatialmultiplexing and demultiplexing weights using received signalmeasurements. In this manner, the signals from the current activesubscriber stations, some of which may be active on the sameconventional channel, are separated and interference and noisesuppressed. When communicating from the base station to the subscriberstations, an optimized multi-lobe antenna radiation pattern tailored tothe current active subscriber station connections and interferencesituation is created. Suitable smart antenna technologies for achievingsuch a spatially directed beam are described, for example, in U.S. Pat.No. 5,828,658, issued Oct. 27, 1998 to Ottersten et al. and U.S. Pat.No. 5,642,353, issued Jun. 24, 1997 to Roy, III et al.

[0022] The outputs of the antennas are connected to a duplexer switch107, which in this TDD system is a time switch. Two possibleimplementations of switch 107 are as a frequency duplexer in a frequencydivision duplex (FDD) system, and as a time switch in a time divisionduplex (TDD) system. When receiving, the antenna outputs are connectedvia switch 107 to a receiver 205, and are mixed down in analog by RFreceiver (“RX”) modules 205 from the carrier frequency to an FMintermediate frequency (“IF”). This signal then is digitized (sampled)by analog to digital converters (“ADCs”) 209. Only the real part of thesignal is sampled. Final down-converting to baseband is carried outdigitally. Digital filters can be used to implement the down-convertingand the digital filtering, the latter using finite impulse response(FIR) filtering techniques. This is shown as block 213. The inventioncan be adapted to suit a wide variety of RF and IF carrier frequenciesand bands.

[0023] There are, in the present example, four down-converted outputsfrom each antenna's digital filter device 213, one per receive timeslot.The particular number of timeslots can be varied to suit network needs.While the present example uses four uplink and four downlink timeslotsfor each TDD frame, desirable results have also been achieved with threetimeslots for the uplink and downlink in each frame. For each of thefour receive timeslots, the four down-converted outputs from the fourantennas are fed to a digital signal processor (DSP) device 217(hereinafter “timeslot processor”) for further processing, includingcalibration, according to one aspect of this invention. Four MotorolaDSP56303 DSPs can be used as timeslot processors, one per receivetimeslot. The timeslot processors 217 monitor the received signal powerand estimate the frequency offset and time alignment. They alsodetermine smart antenna weights for each antenna element. These are usedin the spatial diversity multiple access scheme to determine a signalfrom a particular remote user and to demodulate the determined signal.

[0024] The output of the timeslot processors 217 is demodulated burstdata for each of the four receive timeslots. This data is sent to thehost DSP processor 231 whose main function is to control all elements ofthe system and interface with the higher level processing, which is theprocessing which deals with what signals are required for communicationsin all the different control and service communication channels definedin the system's communication protocol. The host DSP 231 can be aMotorola DSP56303. In addition, timeslot processors send the determinedreceive weights for each user terminal to the host DSP 231. The host DSP231 maintains state and timing information, receives uplink burst datafrom the timeslot processors 217, and programs the timeslot processors217. In addition it decrypts, descrambles, checks error correcting code,and deconstructs bursts of the uplink signals, then formats the uplinksignals to be sent for higher level processing in other parts of thebase station. With respect to the other parts of the base station itformats service data and traffic data for further higher processing inthe base station, receives downlink messages and traffic data from theother parts of the base station, processes the downlink bursts andformats and sends the downlink bursts to a transmitcontroller/modulator, shown as 237. The host DSP also managesprogramming of other components of the base station including thetransmit controller/modulator 237 and the RF timing controller shown as233.

[0025] The RF timing controller 233 interfaces with the RF system, shownas block 245 and also produces a number of timing signals that are usedby both the RF system and the modem. The RF controller 233 reads andtransmits power monitoring and control values, controls the duplexer 107and receives timing parameters and other settings for each burst fromthe host DSP 231.

[0026] The transmit controller/modulator 237, receives transmit datafrom the host DSP 231, four symbols at a time. The transmit controlleruses this data to produce analog IF outputs which are sent to the RFtransmitter (TX) modules 245. Specifically, the received data bits areconverted into a complex modulated signal, up-converted to an IFfrequency, 4-times over-sampled, multiplied by transmit weights obtainedfrom host DSP 231, and converted via digital to analog converters(“DACs”) which are part of transmit controller/modulator 237 to analogtransmit waveforms. The analog waveforms are sent to the transmitmodules 245.

[0027] The transmit modules 245 up-convert the signals to thetransmission frequency and amplify the signals. The amplifiedtransmission signal outputs are sent to antennas 103 via theduplexer/time switch 107.

[0028] User Terminal Structure

[0029]FIG. 2 depicts an example component arrangement in a remoteterminal that provides data or voice communication. The remoteterminal's antenna 45 is connected to a duplexer 46 to permit antenna 45to be used for both transmission and reception. The antenna can beomni-directional or directional. For optimal performance, the antennacan be made up of multiple elements and employ spatial processing asdiscussed above for the base station. In an alternate embodiment,separate receive and transmit antennas are used eliminating the need forthe duplexer 46. In another alternate embodiment, where time divisiondiversity is used, a transmit/receive (TR) switch can be used instead ofa duplexer as is well-known in the art. The duplexer output 47 serves asinput to a receiver 48. The receiver 48 produces a down-converted signal49 which is the input to a demodulator 51. A demodulated received soundor voice signal 67 is input to a speaker 66.

[0030] The remote terminal has a corresponding transmit chain in whichdata or voice to be transmitted is modulated in a modulator 57. Themodulated signal to be transmitted 59, output by the modulator 57, isup-converted and amplified by a transmitter 60, producing a transmitteroutput signal 61. The transmitter output 61 is then input to theduplexer 46 for transmission by the antenna 45.

[0031] The demodulated received data 52 is supplied to a remote terminalcentral processing unit 68 (CPU) as is received data before demodulation50. The remote terminal CPU 68 can be implemented with a standard DSP(digital signal processor) device such as a Motorola series 56300 DSP.This DSP can also perform the functions of the demodulator 51 and themodulator 57. The remote terminal CPU 68 controls the receiver throughline 63, the transmitter through line 62, the demodulator through line52 and the modulator through line 58. It also communicates with akeyboard 53 through line 54 and a display 56 through line 55. Amicrophone 64 and speaker 66 are connected through the modulator 57 andthe demodulator 51 through lines 65 and 66, respectively for a voicecommunications remote terminal. In another embodiment, the microphoneand speaker are also in direct communication with the CPU to providevoice or data communications.

[0032] The remote terminal's voice signal to be transmitted 65 from themicrophone 64 is input to a modulator 57. Traffic and control data to betransmitted 58 is supplied by the remote terminal's CPU 68. Control data58 is transmitted to base stations during registration, sessioninitiation and termination as well as during the session as described ingreater detail below.

[0033] In an alternate embodiment, the speaker 66, and the microphone 64are replaced or augmented by digital interfaces well-known in the artthat allow data to be transmitted to and from an external dataprocessing device (for example, a computer). In one embodiment, theremote terminal's CPU is coupled to a standard digital interface such asa PCMCIA interface to an external computer and the display, keyboard,microphone and speaker are a part of the external computer. The remoteterminal's CPU 68 communicates with these components through the digitalinterface and the external computer's controller. For data onlycommunications, the microphone and speaker can be deleted. For voiceonly communications, the keyboard and display can be deleted.

[0034] Broadcast Channel (BCH)

[0035] In one embodiment, the system of the present invention isinitiated for each user terminal or remote terminal from the broadcastchannel BCH which is transmitted as a burst from the base station to allpotential user terminals. The BCH burst, unlike the traffic channelbursts, is transmitted in all directions where user terminals may be,typically omnidirectionally but the specific beam pattern will depend onthe network. An example of a broadcast burst structure is shown in FIG.3. The BCH communicates enough basic information to enable a subsequentexchange of configuration request CR and configuration message CMbetween the base station and the user terminal. The BCH also providesgeneral frequency offset and timing update information to all userterminals.

[0036] Table 1, below summarizes the content of an example of a BCHburst, as shown in FIG. 3. TABLE 1 Duration Contents  10 μsec ramp - up272 μsec frequency correction training symbols f₁, f₂, . . . , f₁₃₆ 256μsec timing correction training symbols t₁, t₂, . . . t₁₂₈  16 μsecbroadcast preamble r₁, r₂, . . . r₈ 512 μsec information symbols h′₁,h′₂  10 μsec ramp - down  14 μsec inter-burst guard time

[0037] The frequency and timing correction training symbols can be setaccording to any one of many approaches well-known in the art. They canalso be combined, exchanged with a synchronization sequence oreliminated.

[0038] The broadcast information symbols are constructed from a 15-bitbroadcast message which is modulated and coded into a 256 bit sequence.The number of symbols as well as the structure and sequence oftransmitted bits can be varied to suit a wide variety of applications.The broadcast channel information symbols provide the information neededfor a user terminal to request a configuration message from the basestation.

[0039] Each broadcast message is mapped into a broadcast burst with theinformation shown below in Table 2. TABLE 2 Broadcast Message Field # ofBits BStxPwr 5 BSCC 7 BSload 3 Total 15 

[0040] BStxPwr is the effective isotropic radiated power of thebroadcast message. This number indicates the power transmitted by thebase station taking into account the number of amplifiers and diversityantennas available at the base station.

[0041] BSCC is the base station color code, used by the user terminal toselect training data for uplink bursts and to distinguish broadcasts ofdifferent base stations.

[0042] BSload is an indication of the amount of unused capacity the basestation has.

[0043] In one embodiment, the network is designed to take maximaladvantage of spatial division multiple access technologies andparticularly smart antenna array signal processing. To help maintainreliable spatial channels in an extremely dense frequency reuse pattern,the network uses time division duplex TDMA where uplink and downlinktransmissions are always on the same frequency. In addition, becausemany user terminals are single antenna and transmit and receiveomnidirectionally, except for the BCH, an uplink burst is alwaysreceived before a downlink burst needs to be sent. This allows downlinkbursts to be more accurately spatially directed. An uplink trainingsequence is embedded in every uplink burst to allow for moderately fastfrequency hopping despite any decorrelation of the spatial channel withfrequency.

[0044] The frequency hopping sequence may be any one of many differentsequences well-known in the art. In one embodiment, the parameters ofthe frequency hopping scheme are initially unknown to the user terminal.This maximizes the flexibility of the network and increases theflexibility of the user terminal. As explained below, the frequencyhopping parameters are transmitted to the user in the CM burst.

[0045] In one embodiment, the BCH channel is shared by all base stationsin the wireless communication system. Using the 7 bit BSCC, up to 128base stations can be accommodated. The BCH is part of a time divisionduplex channel with a repeating frame. The channel that includes BCH isa single RF carrier frequency used for uplink and downlink. For highnoise environments or for increased robustness, the BCH can hopfrequencies according to a predetermined scheme or be repeated onseveral different frequencies. The repeating frame includes the downlinkBCH for each base station, labeled BS1 etc. as shown in Table 3 below.The next frame includes the uplink Configuration Request CR, labeled CR1etc. and downlink Configuration Message CM, labeled CM1 etc. Each framealso includes a number of reserved slots, shown as empty boxes below.These slots can be used for data traffic, if the broadcast channel isalso used for traffic, for other control messages or reserved to reduceinterference on other channels in the network. In one embodiment, theother traffic channels hop frequencies around and through the BCH. Theframes are repeated for each respective base station 1 to 128 to build asuperframe as discussed in more detail below. After the last CM, CM128,the superframe repeats and begins again with the next superframe and theBCH for base station 1. TABLE 3 Uplink Downlink Superframe 1 Frame 1 BS1Frame 2 CR1 CM1 Frame 3 BS2 Frame 4 CR2 CM2 . . . . . . . . . Frame 255BS128 Frame 256 CR128 CM128 Superframe 2 Frame 1 BS1 Frame 2 CR1 CM1 . .. . . . . . .

[0046] In another embodiment, the BCH is on its own channel and CR andCM are on a separate control channel. Alternately, one BCH can beprovided on a constant frequency and a secondary BCH can be provided onanother channel with hopping frequency. The hopping channel is describedin the CM.

[0047] Registration

[0048] In one embodiment of the present invention, a session begins whena user terminal seeks to register with a base station. The user terminaldoes this without knowing its relative position to the best station interms of direction and distance (or range) to the base station (BS).Therefore, when the user terminal (UT or remote terminal or subscriberstation) requests registration using a configuration request (CR) burst,the base station receives the transmission from the user terminal with alarge timing uncertainty and unknown spatial parameters or weights whencompared to traffic bursts that already utilize timing advancedirectives from the base station.

[0049] Before registration, several user terminals may transmit CRbursts during the same time slot to register with the same base station.CR bursts addressed to different base stations may also be received. Thebase station resolves these requests using spatial processing andmultiple antennas. By combining the multiple antenna measurements(beamforming) the base station minimizes the interference betweensignals and maximizes the signal-to-noise ratio (SNR) of each receivedburst.

[0050] Beamforming can be performed in a variety of ways. In oneembodiment, a training sequence is used with a least-squares costfunction to determine the weights for a beamformer. This allows signalsto be classified as desired or undesired. The training sequence-basedapproach uses an estimation of the timing and frequency offset of the CRburst. This estimation task can be performed by determining theleast-squares cost for each timing and frequency hypothesis. Thisdemands great computational resources. Using a special sequence designand a beamforming algorithm that does not require a search over theentire timing uncertainty range alleviates the computational load of thefull search. In one embodiment, since CR bursts have a high timinginaccuracy, a periodic training sequence is dedicated for CR burstsalone.

[0051] Configuration Request Burst Structure

[0052] A configuration request (CR) burst is transmitted by a userterminal (user terminal) in order to initiate communications orregistration with a base station (base station). It is transmitted aftergathering information about the system by listening to (multiple)broadcast channel (BCH) bursts. The CR burst, is the first communicationfrom a user terminal to the base station and therefore, the userterminal does not have any information about its range to its selectedbase station. Accordingly timing, range, and spatial processing weightsamong other things are all unknown to the base station. An example of aCR burst is shown in FIG. 4.

[0053] The configuration request burst is composed of several fields asshown in FIG. 4 which are listed in Table 4. The durations are describedin terms of microseconds. In one embodiment, a symbol period is 2microseconds. TABLE 4 Configuration Request (CR) Burst fields DurationContents  10 μsec ramp - up 240 μsec training symbols 164 μsecinformation symbols  10 μsec ramp - down 106 μsec extra guard time  15μsec inter-burst guard time

[0054] The training symbols are allocated 240 microseconds in order toallow the signal to be accurately received and demodulated before a userterminal has registered and has received any knowledge of the system.The training symbols are discussed in more detail below.

[0055] The 82 information symbols are constructed from the configurationrequest message using, for example, forward error correction coding. Inthe present embodiment, the CR burst is modulated using π/2-BPSKmodulation in order to decrease the peak-to-average ratio of thetransmitted waveform.

[0056] The information symbols of the present CR burst are mapped out asshown in Table 5, below. Any of the items listed below can be deletedand transmitted later during the registration cycle or not at all basedon the needs of the system. CR is scrambled by a function of BSCCensuring that even if there is some interference from CRs sent to nearbybase stations, the demodulation capture effect of the BSCC works out anycollisions. In one embodiment, the scrambling is performed by taking theencoded bit sequence and exclusive OR'ing it with the output of a linearfeedback shift register. TABLE 5 Configuration Request Message Field #of Bits identity 8 utClass 4 txPwr 5 Total 17 

[0057] identity is a set of unique random bits for each user terminalthat differentiate simultaneous messages from multiple user terminals.Because of the randomness and large number of bits, it is unlikely thattwo user terminals will select the same identity code at the same time.

[0058] utClass identifies user terminal capabilities (highest modulationclass, frequency hopping capabilities, etc. ) This sequence identifiesthe type of user terminal that sent the CR. A palmtop digital assistantmight have different capabilities than a desktop computer with a fixeddedicated antenna. With utClass, the different capabilities can bedistinguished.

[0059] txPwr represents the power used by the user terminal to transmitthe Configuration Request burst. For example, user terminal power=(2txPwr−30) dBm.

[0060] In the present embodiment, the CR burst includes 106 microsecondsof extra guard time. As mentioned above, the CR burst is transmitted bya user terminal without any knowledge of the time required for the burstto travel to the base station. In the present embodiment, the desiredmaximum range from a user terminal to a base station is 15 km. The delayof the burst's reception at the base station includes the delay inreceiving the BCH from the base station. A user terminal at range R kmreceives the BCH burst(s) R/c seconds after they are transmitted by thebase station (c=3×10⁸ m/sec). When the user terminal decides to transmita CR burst, its signal will be delayed by another R/c seconds, so thatthe delay of the CR burst at the base station relative to base stationtime will be 2R/c seconds. To accommodate delays created by a maximumrange of 15 km, the guard period at the end of the CR burst time slotshould be at least 100 microseconds. In addition, in the presentembodiment, the user terminal randomly delays its CR burst transmissionfrom 0 to 9 symbols in order to reduce collisions with other userterminals that are sending CR bursts in the same slot and that may be atabout the same range from the base station. Therefore, a CR burst from adistant user terminal may arrive at the base station as much as 118microseconds late as compared to a user terminal that is very close tothe base station and that does not delay its CR burst transmission. Thisaccounts for the 106 microseconds of extra guard time that is allottedto the CR burst and the extra margin supplied by the 15 microseconds ofinter-burst guard time. With the inter-burst guard time 3 microsecondsof extra margin are allotted before the beginning of the next slot.

[0061] The present embodiment also includes an additional 15microseconds of interburst guard time. This helps to confine the RFenergy from the CR burst to the time-slot allocated for the CR burst inorder not to create adjacent slot interference. The interburst guardtime provides a total guard time of 121 microseconds to reduce thelikelihood that a CR burst will extend into the next time slot.

[0062] The CR burst is sent on the control carrier, as an example,exactly 2265 μsec after receipt of a downlink BCH burst. In this way, anotherwise uninitialized user terminal can send CR without any knowledgeof the frequency hopping sequence parameters. As discussed above, the CRburst is shorter than a standard uplink time-slot to allow for unknowntime-of-flight from the user terminal to the base station and typicallyarrives late in the uplink time-slot receive window.

[0063] Training Sequences

[0064] In the present embodiment, known periodic training sequences areused for the training of base station beamformers in order to extractthe desired CR bursts in the presence of interference. The trainingsequence includes several periodic repetitions of a core sequencefollowed by a marker sequence. Alternatively, the marker sequence mayprecede the repetition of the core sequence. By repeating the coresequence, the search range for a least squares (LS) beamformer can bereduced to a single repetition period of the training sequence. Theperiod of the core sequence is a compromise between the duration of thesearch range and the possibility of finding sequences of the specifiedperiod with good autocorrelation and cross correlation properties. Inthe present embodiment, constraints on the periodicity, mean,autocorrelation and cross correlation are used to define the coresequences of the training sequence for CR burst acquisition.

[0065] Periodicity: x(k+P)=x(k), in which x(k) is the periodic part of aπ/2-BPSK training sequence and P is the period of the sequence. In thepresent example, P=12 symbols.

[0066] Mean: the mean of the periodic sequence is constrained to bezero: ${\frac{1}{P}{\sum\limits_{k = 1}^{P}\quad {x(k)}}} = 0.$

[0067] Autocorrelation: The out-of phase (symbol spaced) autocorrelationis bounded by ⅓, where is the phase offset of the out-of-phase sequence:${\frac{{\sum\limits_{k = 1}^{P}\quad {x*(k){x\left( {k + \tau} \right)}}}}{\sum\limits_{k = 1}^{P}\quad {{x(k)}}^{2}} \leq {1/3}},{\tau \neq 0}$

[0068] Cross correlation: Symbol spaced cross correlation between twocandidate periodic sequences x(k) and y(k) is bounded by ⅓:$\frac{{\sum\limits_{k = 1}^{P}\quad {x*(k){y\left( {k + \tau} \right)}}}}{\sqrt{\sum\limits_{k = 1}^{P}\quad {{x(k)}}^{2}}\sqrt{\sum\limits_{k = 1}^{P}\quad {{y(k)}}^{2}}} \leq {1/3}$

[0069] At least two π/2-BPSK sequences conform to these constraints.More sequences may be possible if the constraints are relaxed. These twosequences are used as the core 12 symbol sequence that is repeated toform the periodic training sequence as discussed below. They are:

[0070] s₁=[1,j,1,j,1,−j,−1,j,−1,−j,−1,−j]

[0071] s₂=[1,j,1,−j,−1,−j,1,j,−1,−j,−1,j]

[0072] The bounds on auto and cross correlations help to make delayedversions of these sequences to appear partially uncorrelated to an LSbeamformer which resolves them.

[0073] The two periodic sequences can be shared among base stations. Inone embodiment, depending on its color code, a base station will acceptone of the two core training sequences but not both. The user terminalwill be able to transmit the correct accepted sequence after learningthe base station color code from the broadcast (BCH) burst. This enablesa reuse pattern of 2. For reuse patterns greater than 2, some of theconstraints on the sequences can be relaxed to yield a larger set ofpossible periodic sequences to distribute among the base stations.

[0074] In an alternate embodiment, the user terminal selects which ofthe core sequences it will transmit. This can aid a base station inresolving two interfering CR bursts. The core sequence can be selectedbased on a serial number, product number, ID number or other storednumber of the user terminal. For, example if the two sequences s₁ and s₂above are available, the user terminal can read its serial numberregister. If the serial number is odd it selects sequence s₁ and if theserial number is even it selects s₂. In another embodiment, the userterminal can generate a random number from 1 to 2. If there are morethan two sequences a greater range of random numbers can be generated.The random number is then mapped into a list of sequences in order toselect the periodic sequence that is associated with the generatedrandom number.

[0075] Transmitting CR Burst and Random Delay

[0076] In one embodiment, the base station transmits broadcast channel(BCH) bursts continuously over a pre-established known channel. To begina session with a desired base station, an unregistered and unrecognizeduser terminal in an unknown location listens to the BCH bursts. From theBCH, it determines the base station with which wants to establishcommunications and selects an appropriate training sequence for thatbase station. It also selects a random number D between 0 and 9, andtransmits its CR burst after delaying it for D symbols. The number forthe delay can be selected as described above with respect to theperiodic training sequence. The user terminal can select an internalregister such as a Serial No. or Product ID No., that contains a numbergreater than 9 and use this as a pointer to select the number D.Alternatively, the user terminal can use a random number generator togenerate a random number between 0 and 9 and apply this number to selectD.

[0077] In one embodiment, the maximum value of random delay D is 9symbols. Therefore, a user terminal can pick one of the 10 randomdelays, {0, 1, 2, . . . , 9} to send its CR burst to the base station.In addition, the maximum allowable roundtrip delay from the base stationto the user terminal is assumed to be 50 symbols. Therefore, a CR burstcan be delayed as much as 59 symbols for a user terminal at the maximumpossible range. This delay is measured with respect to the CR burst of auser terminal that is at zero range and that did not delay itstransmission.

[0078] The base station receives and resolves the CR burst as describedbelow. The roundtrip delay is determined to be 2(R/c)+D microseconds(since a symbol period is 2 microseconds where R km is the range of theuser terminal. The base station, in the Configuration Message (CM)burst, then instructs the user terminal to advance its time by_(a)=(R/c+D/2) microseconds in its response to the CR burst. The basestation is unaware of what, if any delay D the user terminal has appliedto its CR burst. In response to this instruction, the user terminal,knowing its random delay D will subtract out the random delay from thepropagation delay and advance its timing by _(a)−(D/2) microseconds.

[0079] The random delay of D symbols is particularly valuable in amicrocellular setting, or when user terminals cluster at about the samerange from the base station. If the range is about the same for twodifferent user terminals, the CR bursts from the two user terminals willlook identical at the base station and may not be resolved. With randomdelays, the CR bursts will be spaced apart making them easier todistinguish.

[0080] CR Burst Resolution

[0081]FIG. 5 shows a training sequence of a CR burst for one embodimentof the invention. In FIG. 5, x 510 is one of the two core sequences {s₁,s₂}. x is the vector consisting of 12 symbols x₁ to x₁₂. In thisapplication, boldface text is used to represent vectors and normal textis used to represent scalars. The complete CR Burst training sequence isconstructed from the core periodic sequence x. Nine repetitions of x;P1, P2, . . . , P9 are followed by a marker sequence M 505. FIG. 5 alsocan be viewed from the perspective of base station timing. In oneembodiment, FIG. 5 shows windows that the base station uses to resolvereceived training sequences in a CR burst. In this context, thesequences P1 to M would line up with the windows as shown only if thesequences were received from a user terminal that was in the samelocation as the base station, or in other words, if there were nopropagation delay between the base station and the user terminal. Inthis paradigm, a round trip delay margin window 520 contains thesequences P1 through P5 for a total of 60 symbols or 120 microseconds.This accommodates a combined delay of 50 symbols due to the round trippropagation delay between the user terminal and the base station and 10symbols of user terminal selected random delay. A beamformer analysiswindow 530 contains core sequences P6 through P9 and so is 48 symbolswide. This window will capture 4 periods of x even if the CR burst isdelayed by up to 60 symbols.

[0082] Using the observations that fall into the beamformer analysiswindow, a base station can estimate the delay encountered by the CRburst modulo-12 symbols since each period P1 through P9 is identical and12 symbols long. In other words, the measurement in the beamformeranalysis window will be the same for the delays and +12, where 0≦<12.The marker sequence M at the end of the burst can be used to resolvethis modulo-12 ambiguity.

[0083] In order to demodulate the payload part of the burst, theabsolute timing information instead of the relative timing or modulo-12timing information is desired. As mentioned above, the marker sequence(M) at the end of the training sequence of FIG. 5 can be used for thistask. The marker sequence M is set to be M=−x so that one period of thecore training sequence x augmented with M will be orthogonal to twoconcatenated H periods of x, i.e., [x, M] [x,x]^(H)=0 in which x=[x₁, .. . , x₁₂], the core sequence, forms a period of the training sequence.

[0084] Since, in the present embodiment, the maximum allowed delay is 60symbols, a roundtrip delay margin window with a duration of 5 periods ofthe core sequence is provided. This leaves a duration of 4 periods ofthe core sequence for the beamformer analysis window. Absolute timing isdetermined by determining which of the four possible periods of the coresequence is the last one received before the marker sequence. Thebeamformer analysis window may contain portions of five different coresequences, at least three of which are full periods of the coresequence. The first symbol of the found sequence is either 12, 24, 36 or48 symbols from the first symbol of the marker sequence. Therefore theabsolute timing can be determined by testing only five hypotheses. Inother words, given , (0≦<12), as the modulo-12 delay estimate from thespatial processing search, the possible candidates for the absolutedelay are: {, +12, +24, +36, +48}.

[0085] As can be seen from FIG. 5, for any delay less than 60 symbols,the beamformer analysis window at the base station will always containat least 4 periods of the periodic sequence x. As a result, the firstsymbol, x₁, of the first repetition of the core sequence within thebeamforming analysis window can be at most 12 symbols away from theborder of the round trip delay margin window and the beamformer analysiswindow.

[0086] This property of the repeating periodic training sequence can betaken advantage of when searching for the first symbol, x₁, of the coresequence x. FIG. 6 shows a flow diagram for resolving the CR burstaccording to one embodiment of the invention. The CR burst is receivedat the antenna array 602 and the measurements from the multiple antennasfor the period that covers the beamformer analysis window are stored604. Then the beamforming weights that will yield the minimum leastsquares (LS) error for each timing hypothesis in the search window of 12symbols is determined. The least squares error results are used to finda coarse relative timing hypothesis 606. Finding this timing includesperforming a coarse search for the symbol timing modulo-12 andperforming a follow-up search 608.

[0087] A weight vector is then determined 610 using the relative timing.This weight vector is applied to the stored measurements to convert themeasurements from each antenna channel into a single channel 612. Then,this single channel is analyzed to determine the fine timing 614 and thefrequency offset 616 of the desired signal. The fine timing andfrequency estimates are used to determine a new more accurate weightvector 618 based on the data in the beamforming analysis window. Thisimproves the quality of the weight vector and the new weight vector isapplied to the stored measurements to convert the measurements from eachantenna channel into a new single channel 620, further improving thequality of the received signal. The processing so far cannot perfectlydetermine the timing information, because it can only measure timedelays modulo-12 symbols, the duration of the repeating core sequence.The timing estimate is in the range {0 . . . 12}, i.e., delays of and+12 symbols will ideally produce the same timing estimate at this point.Using the new weight vector, absolute timing is determined by findingthe marker sequence 622. This resolves the modulo-12 timing ambiguity.

[0088] When the absolute timing is known, the entire training sequencecan be identified. Accordingly a new weight vector calculation can bemade using the entire training sequence including the marker sequence624. This redetermined weight vector is still more accurate because ofthe larger number of samples that can be used. It is applied to thestored measurements to again convert the measurements from each antennachannel into a single channel 626. With the new single channel, the CRburst is demodulated and read 628.

[0089] This processing structure yields accurate beamformer weights thatcan be used to receive the desired signal without determining perfecttiming for the signal.

[0090] Coarse Search for Relative Timing

[0091] After the CR burst has been received in each of the antennas ofthe array 602 and the signals have been stored 604. The system canproceed to determine the relative timing based on the storedmeasurements 606. In one embodiment, this process is done using acovariance matrix computation and a Cholesky decomposition.

[0092] For measurements that lie in the beamforming analysis windowassume that measurements are collected at 1.5 times the symbol rate. Inthis example, the beamforming analysis window is of duration 48 symbolsor 4 repetitions or periods of the core sequence. Next, assume that thevariable coreSnapPoint points to the first snapshot that is in thebeamformer analysis window, and r(t) denotes the snapshot (measurementvector) collected at time t seconds after the start of the CR burst(relative to base station time). The covariance matrix R can beestimated as follows, where T_(BAW) is the time of the beamforminganalysis window:${R = {\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{r(t)}{r^{H}(t)}}}},{T_{BAW} = \left\{ {t\left. {{coreSnapPoint} \leq t < {{coreSnapPoint} + 48}} \right\}} \right.}$

[0093] After computing the covariance matrix R, a matrix L can be foundsuch that

R=LL^(H)

[0094] L is termed as the Cholesky factor of R.

[0095] In one embodiment, the location of the first symbol of the coretraining sequence over the first 12 symbols of the beamforming searchwindow is searched for using a least-squares processor with a searchstep of ⅔ symbols. This results in 18 possible locations of the firstsymbol, i.e. 18 hypotheses and, accordingly, 18 least-squares (LS) errorcalculations. The vector coarseSearchGrid contains the delay hypothesisvalues for each ⅔ symbol increment (The unit used here is a symbolperiod):

[0096] coarseSearchGrid=[0,⅔,{fraction (4/3)},2, . . . ,11 ⅓] whichcontains the delay values for the 18 hypotheses.

[0097] For each delay hypothesis k, (1≦k≦18), the following computationsare performed:

[0098] Calculate cross-correlation vector p_(k) for each hypothesis:$p_{k} = {\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{r(t)}{{*\left( {t + \tau_{k}} \right)}}}}$

[0099] In which r(t) is the received signal samples and d(t) is thesamples of the desired signal. The desired signal samples are assumed tobe available in a filter bank over-sampled at 24 times the symbol rate.The value k is the assumed delay for the k-th hypothesis, i.e.,k=coarseSearchGrid (k).

[0100] Back Substitution: The resulting vector p_(k) is applied to solvefor an interim vector x_(k) for each hypothesis k, where L is theCholesky factor as mentioned above:

Lx_(k)=p_(k)

[0101] Then the least-squares (LS) fit for each hypothesis is computed:$f_{k} = {{f\left( \tau_{k} \right)} = {{\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{d\left( {t + \tau_{k}} \right)}}^{2}} - {X_{k}^{H}X_{k}}}}$

[0102] Due to the periodicity of the desired signal within thebeamforming analysis window, the cross correlation vector computationcan be modified to:$p_{k} = {\sum\limits_{t\quad \varepsilon \quad T_{1}}{\left\lbrack {{r(t)} + {r\left( {t + 12} \right)} + {r\left( {t + 24} \right)} + {r\left( {t + 36} \right)}} \right\rbrack d*\left( {t + \tau_{k}} \right)}}$

[0103] in which T₁ is a period of the desired signal, i.e.,

[0104] T₁={t|coreSnapPoint≦t<coreSnapPoint+12}

[0105] Therefore, the above calculation of the cross correlation vectorP_(k) costs one-fourth as many multiplies as it would if the coresequence were not a repeated periodic sequence within the trainingsequence. Finally, the hypothesis with the minimal LS error f_(k) ispicked. An illustration is presented with respect to FIG. 7.

[0106]FIG. 7 shows the LS cost function on the vertical axis 702 as afunction of the time delay for the 18 hypotheses on the horizontal axis704. The horizontal axis is marked in units of ⅔ of a symbol time inaccord with the sampling rate of 1.5 times the symbol rate. The selectedbest coarse search time delay estimate 706 is shown in FIG. 7 at={fraction (4/3)} symbols. Note that the delay is measured with respectto the nominal time or modulo-12 time at which the CR burst is expectedto arrive. This nominal time is named the coreSnapPoint. This simplifiedcomputation of the cross correlation vectors p_(k) based on theperiodicity of the training sequence within the beamforming analysiswindow yields substantially the same accuracy as a regular crosscorrelation computation. Any mismatch of the training sequence in thissimplified approach makes only a minimal impact on the performance ofthe beamformers due to the periodicity of the training sequence.

[0107] Follow-Up Search

[0108] Having made a coarse determination of the relative timing 606 afollow-up timing search 608 can be performed. This search has one moreLS error calculation. The result of this calculation can be compared tothe best LS error from the coarse search.

[0109] The LS error vector f_(k) from the coarse search is treated as acircular buffer and concentration is on the midpoint of the rangebetween the best location from the coarse search (that yielded theminimum LS error) and its neighbor that yielded the next best LS error.

[0110] In the coarse search, the following 20 dimensional vectors wereformed:

[0111] updatedLSValues=[f₁₈,f₁,f₂,f₃,f₄, . . . , f_(17,f) ₁₈, f₁]and

[0112] updatedCoarseSearchGrid=[−{fraction (2/3)},0,{fraction(2/3)},{fraction (4/3)},3 {fraction (1/3)}, 4, . . . , 11 {fraction(1/3)}, 12]

[0113] Assume that the hypothesis of f₃ (={fraction (4/3)}) (of thecurrent list) was selected by the coarse search procedure (as shown inFIG. 5) because f₃<f₂<f₄. In the follow-up search procedure, the LSerror is computed for =1, since this forms the midpoint of the rangebetween the delays corresponding to f₂ (=⅔) and f₃ (={fraction (4/3)}).This is shown graphically in FIG. 8.

[0114]FIG. 8 shows the LS cost function 802 as a function of the 18hypotheses 804 in which the time domain is again sampled at a rate of1.5 times the symbol rate. The selected best case coarse search timedelay estimate 806 is ={fraction (4/3)} symbols. After the additionalhypothesis test, the hypothesis (among the 19 of them) which correspondsto the minimum least-squares error is again picked. In this example,_(o)=1 is the delay value 808 that accomplishes this.

[0115] Beamforming Weights

[0116] After the follow-up search, determining the relative timing delayτ to within one third of a symbol period 608, the weight vector w_(o) isrecomputed to extract the desired signal as follows:

[0117] Using the cross-correlation vector p_(o) for the best hypothesis:$p_{o} = {\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{r(t)}d*\left( {t + \tau_{0}} \right)}}$

[0118] And the corresponding interim vector x_(o):

Lx_(o)=p_(o)

[0119] The weights can be computed by solving the following backsubstitution:

L^(H)w_(o)=p_(o)

[0120] With the resulting LS error which is already determined to bef(_(o)):${{f\left( {}_{\quad o} \right)} = {{\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{d\left( {t +_{o}} \right)}}^{2}} - {x_{o}^{H}x_{o}}}}\quad$

[0121] The beamforming operation results in a single channel measurementthat shall be named g(t) and defined as follows:

g(t)=w _(o) ^(H) r(t)

[0122] The actual computations can be simplified because the time rangeof the beamforming operation does not need to be the whole burst. Notethat the frequency estimation (search) has not yet been performed. Thisreduces the search to a single dimension, namely time-delay. Thefrequency search can be avoided because of the duration of thebeamforming analysis window, the maximum frequency deviation expected inthe received signal and the target SNR level at the output of thebeamformer. When the beamformer analysis window is short enough to makethe frequency offset negligible, the desired signal mismatch is notsignificant enough to degrade performance. Furthermore, the inability toimprove the SNR even by using an MSE beamformer (that knows the perfectcovariance matrix and steering vector) to high levels (above 5 dB) makesthe actual beamformer blind to imperfections in the desired signal (suchas frequency offset). The presence of frequency offset becomes seriousat high target SNRs and ignoring large frequency offsets causes the SNRperformance to tend to saturate at around 5 dB output SNR. However, thisis still not an issue if the CR burst payload can withstand SNRs as lowas 0 dB. Furthermore, the single channel estimation of frequency andfine timing that follows will alleviate these problems using fewercomputations.

[0123] Fine Timing Estimator

[0124] The coarse search and the follow-up search provide a timing delaywith an effective rate of three times the symbol rate. The timingresolution can be improved to better demodulate the payload. Severeintersymbol interference can be expected at the worst case timing events(⅙ symbol period of timing error). To estimate fine timing 614, theOerder-Meyr blind timing estimator can be used. This estimator is blindin the sense that it does not assume any knowledge of the transmittedsymbols. Therefore it is insensitive to frequency offset errors. TheOerder-Meyr estimator can be used as follows:

[0125] First, interpolate g(t) to 3 times the symbol rate (from 1.5times the symbol rate) using an interpolation filter, and call theoutput gi(t). The duration of the measurements process amounts to48+12+82=144 symbol periods, this is the guaranteed maximum number ofsymbols on the right hand side of the coarse timing estimate in thebeamforming analysis window as shown in FIG. 5. Alternatively, thesymbols can be sampled at a three times rate originally. In such a case,only every other sample would be used in the coarse search and follow-upsearch.

[0126] Next, the interpolated signal is passed through a memorylessnonlinearity to obtain

g _(n)(t)=|g _(i)(t)|.

[0127] The absolute value nonlinearity generates tones at the multiplesof the symbol rate. The nonlinearity is approximated by fitting apolygon. For example, if z is a complex number with representationz=z_(r)+jz_(i), then |z|≈max(|z_(r)|,|z_(i)|)+0.34×min(|z_(r)|,|z_(i)|). The zero-crossing of the complex sine wave at thesymbol rate is determined by using a 3 point DFT and this location istermed as a symbol transmission instant. Finally, the symboltransmission instant is found that is closest to the position identifiedby the follow-up search as the location for the first symbol of theperiodic training sequence.

[0128] The closed-form estimate obtained using the Oerder-Meyr timingestimator is termed as _(fine). If this estimate is not in the range(0,12), it is mapped into this range by adding or subtracting 12 to it.

[0129] Coarse Frequency Estimator

[0130] After fine timing is acquired 614, the measurements are used inthe analysis window together with the desired signal to compute thecross correlation function and determine the coarse frequency estimate616 as the peak of the cross correlation function. For simplicity, thisanalysis is done at the 1.5 times over sampling rate (instead of the 3times rate used for the fine timing search), however many other samplingrates can be used. Specifically, for the m-th frequency hypothesis, thefunction freqmatch(m) is computed:${{freqMatch}(m)} = {{\sum\limits_{t\quad \varepsilon \quad T_{BAW}}{{g(t)}d*\left( {t + \tau_{fine}} \right){\exp \left( {{- {j2\pi}}\quad f_{m}t} \right)}}}}^{2}$

[0131] The frequency candidate that maximizes freqmatch(m) is selectedas the frequency estimate, f_(coarse). Frequency candidates (f_(m)'s)are in the set:

[0132] {−2800,−2000,−1200,−400,400, 1200, 2000,2800}

[0133] Alternatively, the frequency uncertainty can be regarded as muchless and fewer hypothesis tests can be performed.

[0134] More Accurate Beamforming

[0135] Using the frequency and timing estimates _(fine), f_(coarse), animproved weight vector, w_(final) can be determined 618 and applied tothe found core sequences to obtain an estimate of the desired burstŝ(t):

ŝ(t)=w _(final) ^(H) r(t)

[0136] The more accurate weight vector is obtained by employingd(t+_(fine))exp (j2πf_(fine)t) as the desired signal in the LS errorcomputations. However, if the corresponding LS error is larger than thefollow up search based LS error f_(o), the fine timing and frequencyestimates are rejected and the estimates are set to _(fine)=_(o) andf_(coarse)=0, which results in w_(final)=w_(o).

[0137] To further improve the SNR results at high post-copy SNR levels,the search can be performed for a fine frequency estimate around thecoarse frequency estimate at locations f_(coarse)+[−800,0,800] using anLS fit to multichannel measurements for tεT_(BAW). Such a search can beincluded to improve the frequency estimation performance for the CRburst demodulator.

[0138] Absolute Timing Recovery

[0139] Prior to determining the absolute timing, as opposed to relativetiming, the more accurate weight vector is applied in order to convertthe measurements stored from each of the antennas into a single channelmeasurement 620. This conversion is still done using the data in thebeamforming analysis window because only this data is certain to consistonly of periods of the core sequence. An appropriate procedure 622 fordetermining the absolute delay can be implemented as follows. Assumethat the modulo-12 time-delay estimate is, and that g(t) denotes theoutput of a beamformer (as described above g(t) is a single channelmeasurement) that extracts the desired CR burst. First, the candidatestarting locations for the concatenated sequence [P9,M] (see FIG. 5) foreach of the five delay hypotheses is determined. For example, if theabsolute delay equals, the sequence [P9,M] should start +36 symbols awayfrom the left border of the beamformer analysis window. For thehypothesis in which the absolute delay is assumed to be equal to +48,the sequence [P9, M] should start 84 symbols away from the left borderof the analysis window.

[0140] More specifically, assume that T_(k) denotes the begin time forthe k-th hypothesis, i.e., T_(k)=+36+(12×k), for k=0, 1, 2, 3, 4. Letv_(k) denote the samples of g(t) that correspond to the interval whichstarts at T_(k) for a duration of 24 symbols (two periods). For eachhypothesis, compute:

h(k)=|v _(k) [x,−x] ^(H)|².

[0141] Pick the hypothesis that yields the maximum h(k).

[0142] Assume that hypothesis k_(o) is selected. Then, the absolutetiming estimate is determined as +(k_(o)×12).

[0143] Due to the orthogonal nature of [x, m] and [x, x], there is afive-ary pulse-position modulation (PPM) demodulation problem in whichthe SNR changes depending on the true position of the desired vector [x,m]. For example, if the actual delay is less than a period, then thepayload portion of the desired CR burst will appear as noise for thehypothesis tests 1, 2, 3, 4. On the other hand, if the actual delay is,for example 20 symbols, then, the CR burst payload symbols will notcontribute to the test of a hypothesis in which k=0 as noise because ofthe orthogonality of [x, m] and [x, x], but they will contribute to thenoise component in h(k) for k=2, 3, 4. With this delay condition, thebeamforming analysis window receives the following 48 symbols:

[0144] x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,x₁,x₂,x₃,x₄, . . .x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x_(12,x) ₁,x₂,x₃,x₄,

[0145] In this stream, the first and last 12 symbols are written out.The spatial processing search will discover the first occurrence of x₁at a delay of 8 symbols. The next step is to determine whether theabsolute delay is 8, 20, 32, 44, 56 symbols. In order to determine this,the measurements following the beamforming analysis window are focusedupon. With a delay of 20 symbols, the next 40 symbols will be:

[0146]x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,x₁,x₂,x₃,x₄,x₅,x₆,x₇,x₈,x₉,x₁₀,x₁₁,x₁₂,−x₁,−x₂,−x₃,−x₄,−x₅,−x₆,−x₇,−x₈,−x₉,−x₁₀,−

[0147] x₁₁,−x₁₂,d₁,d₂,d₃,d₄,d₅,d₆,d₇,d₈

[0148] in which d_(i) indicates the i-th payload symbol, which isunknown. As a result, v₀=[x, x] and v₁=[x, −x], which results in h(0)=0and h(1)=24². Accordingly, the desired signal does not contribute to thedecision variable h(0) when the absolute delay is larger than 12. On theother hand, v₂=[−x₁,−x₂, . . . , −x₁₂, d₁,d₂, . . . d₁₂] is notnecessarily equal to zero. The first half of v₂ equals the markersequence, which yields the result:

h(2)=|−12−[d ₁ ,d ₂ , . . . d ₁₂ ]x ^(H)|².

[0149] This differs significantly from:

h(3)=|[d ₁ ,d ₂ , . . . d ₁₂ ]x ^(H) −[d ₁₃ ,d1 ₁₄ , . . . , d ₂₄ ]x^(H)|².

[0150] h(2) is expected to be higher than h(3) on average because of thecoherence term (−12) inside the magnitude operator and its presencecreates a significant competition to the correct hypothesis decisionvalue (h(0)) in the presence of measurement noise. Therefore, absolutedelay errors that are equal to +12 should dominate other values of delayestimation errors. One way to eliminate the self-noise problem is to putthe marker sequence in the beginning of the burst and search for theconcatenated sequence [−x, x]. In such a design, self noise will existonly due to the presence of the ramp-up symbols, but this will affectthe noise component in only one of the h(k)'s. Other modifications tothe ordering of the sequences are also possible to suit particularapplications.

[0151] As discussed above, the remaining task is to find the markersequence. This can be done based on a cross correlation operation withthe 1.5 times over-sampled version of the sequence [x,-x] with v_(k)corresponding to all of the five hypotheses locations indicating periodslips of 0, 1, 2, 3, 4.

[0152] Using the fine timing estimate _(fine), the time of the finalbeamformer output sample (that arrives at t_(c)) which is closest tocoreSnapPoint+_(fine) is determined. Let _(e) denote the time differencebetween the chosen measurement at t_(c) and the location of actualtiming location:

_(e) =t _(c) −coreSnapPoint− _(fine)

[0153] Remember that the beginning of the k-th hypothesis (k=0, 1, 2, 3,4) will be at times T_(k)=coreSnapPoint+_(fine). Therefore, the vectorv_(k) to be tested for the cross correlation for the k-th hypothesiswill take the form:

v _(k) =[ŝ(t _(c)+12×(3+k)), {circumflex over (s)}(t _(c)+12×(3+k)+⅔)],ŝ(t _(c)+12×(3+k)+2×⅔), . . . , ŝ(t _(c)+12×(3+k)+35×⅔)

[0154] which is a vector with 36 entries.

[0155] The v_(k)'s are cross correlated with the desired signal vectord, which is formed from the knowledge of the training waveform and thetiming difference _(e):

d=[s _(d)(coreSnapPoint+ _(e)+12×3), s _(d)(coreSnapPoint+ _(e)+12×3+⅔),. . . , s _(d)(coreSnapPoint+ _(e)+12×3+35×⅔)]

[0156] in which s_(d)(t) is the training waveform for the desiredsignal.

[0157] The magnitude squared cross correlations for each hypothesis iscomputed:

h(k)=|v _(k) d ^(H)|²

[0158] Let k_(o) denote the index of the largest h(k). Then, theabsolute timing is determined as:

_(abs)=_(fine)+(k _(o)×12)

[0159] The values are in terms of symbol durations in the above equationwith the period of the training sequence being 12 symbols.

[0160] Alternatively, symbol spaced sampling can be used in the absolutetiming recovery. This can eliminate the mismatches created in the 1.5times measurements that result in loss of orthogonality. With symbolspaced sampling, this operation will require 5 cross correlations oflength 24 and comparing the squared-magnitudes of the crosscorrelations.

[0161] After absolute timing recovery 622, the whole training sequencecan be used to improve the timing and frequency estimates and theseestimates can be used to perform one more stage of beamforming over thewhole training sequence duration. This can increase the number ofsymbols used in spatial processing to 120 symbols from 48 and improvethe performance at a cost of computational complexity The beamformingwould involve first determining a still more accurate weight vectorusing the full training sequence 626 and then applying this weightvector to convert the measurements stored for each antenna channel intoa single channel measurement 628. In doing so a new covariance matrixshould be computed and therefore another Cholesky factorizationperformed. The conversion can be applied to the entire CR burst so thatthe CR burst can be demodulated as a single channel 628. Alternatively,the absolute timing can be applied to determine the beginning and end ofthe CR burst and the existing weight vector and frequency estimates canbe used to demodulate the signal. The choice will depend on the demandsof the particular system and the condition of the channel. Havingdetermined timing and a weight vector, this weight vector can be used tosend traffic back to the remote from which the CR burst was received630.

[0162] General Matters

[0163] The present invention can eliminate the need to acquire theabsolute timing information in order to perform beamforming. It exploitsthe periodicity of target training sequences in order to estimate thetime delay encountered by the desired signal modulo-the period of thetraining sequence which is less than the total time delay ambiguityrange. The reception of uplink messages at the base station which arenot perfectly synchronized is enhanced.

[0164] Training based interference cancellation methods can be used toenhance the signal quality for such bursts. However, the trainingsequence should be aligned with the incoming signal, and therefore theresulting search process involves testing every possible delay with apredetermined resolution. As the delay ambiguity grows, this hypothesistesting process becomes increasingly more expensive with computationalresources.

[0165] Using a periodic training sequence eases the efforts ofhypothesis testing followed by a timing acquisition sequence todetermine the perfect timing information. The periodic sequencedecreases the timing ambiguity to within a period of the trainingsequence, which can be selected small so that resources are available tohandle the hypothesis testing task. For example, if the expected delayis 50 symbols, and if the period of the training sequence is 10 symbols,with a resolution of a symbol, 10 hypotheses can be tested instead of50, provided that the periodic training sequence can be observed in thesearch window, regardless of the delay. In addition, the searchoperation, which involves cross correlations can be simplified by thenumber of periods in the search window, if the search window contains 5periods of the training sequence (period with 10), the crosscorrelations can be simplified by five-fold.

[0166] Once the timing hypothesis is verified, only the number ofperiods of the repeating core sequence that has been skipped must bedetermined. To perform this more accurately, the multiple channelmeasurements (if available) can be converted to a single channelmeasurement using the search procedure results outlined above. Afterthat a timing acquisition sequence that is at the beginning of the burstcan be found, and to find the number of periods that were missed. So inthe previous example, only periods {0, 1, 2, 3, 4} may have been missedin the beamforming analysis window. Accordingly, 5 searches can beperformed and these are performed on single channel measurements ratherthan multichannel measurements.

[0167] The invention eliminates the high cost of search on possiblymultichannel data for all possible delays that may be encountered by theuser terminal as a function of range. The burst structure and periodictraining sequence makes it easier to search for the arrival time of thesignal and the periodicity of the training further reduces the cost ofcomputations.

[0168] In the description above, for the purposes of explanation,numerous specific details are set forth in order to provide a thoroughunderstanding of the present invention. It will be apparent, however, toone skilled in the art that the present invention may be practicedwithout some of these specific details. In other instances, well-knownstructures and devices are shown in block diagram form.

[0169] The present invention includes various steps. The steps of thepresent invention may be performed by hardware components, such as thoseshown in FIGS. 1 and 2, or may be embodied in machine-executableinstructions, which may be used to cause a general-purpose orspecial-purpose processor or logic circuits programmed with theinstructions to perform the steps. Alternatively, the steps may beperformed by a combination of hardware and software. The steps have beendescribed as being performed by either the base station or the userterminal. However, any steps described as being performed by the basestation may be performed by the user terminal and vice versa. Theinvention is equally applicable to systems in which terminalscommunicate with each other without either one being designated as abase station, a user terminal, a remote terminal or a subscriberstation.

[0170] The present invention may be provided as a computer programproduct which may include a machine-readable medium having storedthereon instructions which may be used to program a computer (or otherelectronic devices) to perform a process according to the presentinvention. The machine-readable medium may include, but is not limitedto, floppy diskettes, optical disks, CD-ROMs, and magneto-optical disks,ROMs, RAMs, EPROMs, EEPROMs, magnet or optical cards, flash memory, orother type of media/machine-readable medium suitable for storingelectronic instructions. Moreover, the present invention may also bedownloaded as a computer program product, wherein the program may betransferred from a remote computer to a requesting computer by way ofdata signals embodied in a carrier wave or other propagation medium viaa communication link (e.g., a modem or network connection).

[0171] Importantly, while the present invention has been described inthe context of a wireless internet data system for portable handsets, itcan be applied to a wide variety of different wireless systems in whichdata are exchanged. Such systems include voice, video, music, broadcastand other types of data systems without external connections. Thepresent invention can be applied to fixed remote terminals as well as tolow and high mobility terminals. Many of the methods are described intheir most basic form but steps can be added to or deleted from any ofthe methods and information can be added or subtracted from any of thedescribed messages without departing from the basic scope of the presentinvention. It will be apparent to those skilled in the art that manyfurther modifications and adaptations can be made. The particularembodiments are not provided to limit the invention but to illustrateit. The scope of the present invention is not to be determined by thespecific examples provided above but only by the claims below.

What is claimed is:
 1. A training sequence for a radio communicationssystem comprising: a core sequence of symbols; a successive repetitionof the core sequence; and a marker sequence having sequence of symbolsdifferent from the core sequence.
 2. The training sequence of claim 1wherein the core sequence is transmitted as binary symbols and themarker sequence is equal and opposite in sign to the core sequence. 3.The training sequence of claim 1 wherein the core sequence augmentedwith the marker sequence forms a vector that is orthogonal to a vectorformed by the core sequence augmented with the core sequence.
 4. Thetraining sequence of claim 1 wherein the marker sequence follows therepetition of the core sequence.
 5. The training sequence of claim 1wherein the marker sequence precedes the repetition of the coresequence.
 6. The training sequence of claim 1 wherein the repetition ofthe core sequence has a duration longer than the maximum round tripdelay time from a terminal transmitting the training sequence to aterminal receiving the training sequence and back.
 7. The trainingsequence of claim 1 wherein the repetition of the core sequence has aduration longer than a duration of a beam forming analysis window plusthe maximum round trip delay time from a terminal transmitting thetraining sequence to a terminal receiving the training sequence andback.
 8. The training sequence of claim 1 wherein the repetition of thecore sequence has a duration longer than the maximum round trip delaytime from a terminal transmitting the training sequence to a terminalreceiving the training sequence and back plus a random delay applied bythe terminal transmitting the training sequence.
 9. The trainingsequence of claim 1 wherein the repetition of the core sequencecomprises a repetition of the core sequence successively a specifiednumber of times.
 10. The training sequence of claim 1 wherein the coresequence consists essentially of 12 symbols.
 11. The training sequenceof claim 1 wherein the core sequence has a normalized cross-correlationof about ⅓.
 12. The training sequence of claim 1 wherein the coresequence has a normalized autocorrelation of about ⅓.
 13. The trainingsequence of claim 1 wherein the absolute value of the mean of th e coresequence is about zero.
 14. A method comprising: generating a coresequence of symbols; generating a successive repetition of the coresequence; and generating a marker sequence having sequence of symbolsdifferent from the core sequence; combining the repetition of the coresequence and marker sequence to form a training sequence; andtransmitting the training sequence with a communications burst in aradio communications system.
 15. The method of claim 14 whereintransmitting the training sequence comprises transmitting binary symbolsand wherein generating the marker sequence comprises generating a markersequence that is equal and opposite in sign to the core sequence. 16.The method of claim 14 wherein the core sequence augmented with themarker sequence forms a vector that is orthogonal to a vector formed bythe core sequence augmented with the core sequence.
 17. The method ofclaim 14 wherein the repetition of the core sequence has a durationlonger than the maximum round trip delay time from a terminaltransmitting the training sequence to a terminal receiving the trainingsequence and back.
 18. The method of claim 14 wherein the core sequencehas a normalized cross-correlation of about ⅓.
 19. The method of claim14 wherein the core sequence has a normalized autocorrelation of about⅓.
 20. The method of claim 14 wherein the absolute value of the mean ofthe core sequence is about zero.
 21. A machine-readable medium havingstored thereon data representing sequences of instructions which, whenexecuted by a machine, cause the machine to perform operationscomprising: generating a core sequence of symbols; generating asuccessive repetition of the core sequence; and generating a markersequence having sequence of symbols different from the core sequence;combining the repetition of the core sequence and marker sequence toform a training sequence; and transmitting the training sequence with acommunications burst in a radio communications system.
 22. The medium ofclaim 21 wherein transmitting the training sequence comprisestransmitting binary symbols and wherein generating the marker sequencecomprises generating a marker sequence that is equal and opposite insign to the core sequence.
 23. The medium of claim 21 wherein the coresequence augmented with the marker sequence forms a vector that isorthogonal to a vector formed by the core sequence augmented with thecore sequence.
 24. The medium of claim 21 wherein the repetition of thecore sequence has a duration longer than the maximum round trip delaytime from a terminal transmitting the training sequence to a terminalreceiving the training sequence and back.
 25. The medium of claim 21wherein the core sequence has a normalized cross-correlation of about ⅓.26. The medium of claim 21 wherein the core sequence has a normalizedautocorrelation of about ⅓.
 27. The medium of claim 21 wherein theabsolute value of the mean of the core sequence is about zero.